# NUMBERS IN STANDARD FORM WORKSHEET

Problems 1-7 : Write the given number in standard form.

Problem 1 :

50000

Problem 2 :

4800

Problem 3 :

61700000

Problem 4 :

0.00000006

Problem 5 :

0.000574

Problem 6 :

37341000000

Problem 7 :

0.000000000000412

Problem 8 :

(2.05 x 105) x (8.17 x 103)

Problem 9 :

(4 x 105) x (2 x 104)

Problem 10 :

(5 x 106) x (7 x 108)

Problem 11 :

(3 x 104) ÷ (6 x 10-3)

Problem 12 :

(2.1 x 10-5) ÷ (7 x 10-4)

Problem 13 :

(5 x 104)2

Problem 14 :

(2.5 x 103) + (9.8 x 103)

Problem 15 :

(2.78 x 102) + (5.63 x 105)

Problem 16 :

(7.58 x 102) + (6.45. x 10-1)

Problem 17 :

(5.64 x 103) - (3.98. x 103)

Problem 18 :

(3.99 x 102) - (4.7. x 10-2)

Problem 19 :

Write three hundred thousand in standard form.

Problem 20 :

Write five million in standard form.

Problem 21 :

Work out five million multiplied by three hundred thousand. Give your answer in standard form.

Problem 22 :

How many grams are there in 2500 kilograms? Give your answer in standard form. In 50000, there is no decimal point. So, assume there is a decimal point at the end.

50000.

Add the decimal point after the first nonzero digit.

5.0000

Count the number of digits that the decimal point is shifted. The decimal point is shifted four digits to the left. Take 4 as exponent for 10 and 104 can be used to write the given number in standard form.

50000 = 5.0 x 104

In 4800, there is no decimal point. So, assume there is a decimal point at the end.

4800.

Add the decimal point after the first nonzero digit.

4.800

The decimal point is shifted three digits to the left. Take 3 as exponent for 10 and 103 can be used to write the given number in standard form.

4800 = 4.8x 103

In 61700000, there is no decimal point. So, assume there is a decimal point at the end.

61700000.

Add the decimal point after the first nonzero digit.

6.1700000

The decimal point is shifted seven digits to the left. Take 7 as exponent for 10 and 107 can be used to write the given number in standard form.

61700000 = 6.17x 107

0.00000008

Add the decimal point after the first nonzero digit.

8.0

The decimal point is shifted eight digits to the right. Take -8 as exponent for 10 and 10-8 can be used to write the given number in standard form.

0.00000008 = 8.0 x 10-8

0.000574

Add the decimal point after the first nonzero digit.

5.74

The decimal point is shifted four digits to the right. Take -4 as exponent for 10 and 10-4 can be used to write the given number in standard form.

0.000574 = 5.74 x 10-4

In 37341000000, there is no decimal point. So, assume there is a decimal point at the end.

37341000000.

Add the decimal point after the first nonzero digit.

3.7341000000

The decimal point is shifted ten digits to the left. Take 10 as exponent for 10 and 1010 can be used to write the given number in standard form.

37341000000 = 3.7341 x 1010

0.000000000000412

Add the decimal point after the first nonzero digit.

4.12

The decimal point is shifted thirteen digits to the right. Take -13 as exponent for 10 and 10-13 can be used to write the given number in standard form.

0.000000000000412 = 4.12 x 10-13

= (2.05 x 105) x (8.17 x 103)

= (2.05 x 8.17) x (10103)

= 16.7485 x 105 + 3

= 16.7485 x 108

= 1.67485 x 10108

= 1.67485 x 101 + 8

= 1.67485 x 109

= (4 x 105) x (2 x 104)

= (4 x 2) x (10104)

= 8 x 105 + 4

= 8.0 x 109

= (5 x 106) x (7 x 108)

= (5 x 7) x (10108)

= 35 x 106 + 8

= 35 x 1014

= 3.5 x 101014

= 3.5 x 101 + 14

= 3.5 x 1015

= (3 ÷ 6) x (104 ÷ 10-3)

= 0.5 x 104 - (-3)

= 0.5 x 104 + 3

= 0.5 x 107

= 5.0 x 101 x 107

= 5.0 x 101 + 7

= 5.0 x 108

= (2.1 x 10-5) ÷ (7 x 10-4)

= (2.1 ÷ 7) x (10-5 ÷ 10-4)

= 0.3 x 10-5 - (-4)

= 0.3 x 10-5 + 4

= 0.3 x 10-1

= 3.0 x 101 x 10-1

= 3.0 x 101 + (-1)

= 3.0 x 101 - 1

= 3.0 x 100

= (5 x 104)2

= (5 x 104)(5 x 104)

= (5 x 5)(10x 104)

= 25 x 104 + 4

= 25 x 108

= 2.5 x 10x 108

= 2.5 x 101 + 8

= 2.5 x 109

= (2.5 x 103) + (9.8 x 103)

Factor 103.

= (2.5 + 9.8) x 103

= 12.3 x 103

= 1.23 x 10x 103

= 1.23 x 101 + 3

= 1.23 x 104

= (2.78 x 102) + (5.63 x 105)

= (0.00278 x 10x 102) + (5.63 x 105)

= (0.00278 x 103 + 2) + (5.63 x 105)

= (0.00278 x 105) + (5.63 x 105)

Factor 103.

= (0.00278 + 5.63) x 105

= 5.63278 x 105

= (7.58 x 102) + (6.45 x 10-1)

= (7.58 x 102) + (0.00645 x 10x 10-1)

= (7.58 x 102) + (0.00645 x 103 + (-1))

= (7.58 x 102) + (0.00645 x 103 - 1)

= (7.58 x 102) + (0.00645 x 102)

Factor 102.

= (7.58 + 0.00645) x 102

= 7.58645 x 102

= (5.64 x 103) - (3.98. x 103)

Factor 103.

= (5.64 - 3.98) x 103

= 1.66 x 103

= (3.99 x 102) - (4.7. x 10-2)

= (3.99 x 102) - (0.00047 x 10x 10-2)

= (3.99 x 102) - (0.00047 x 104 + (-2))

= (3.99 x 102) - (0.00047 x 104 - 2)

= (3.99 x 102) - (0.00047 x 102)

Factor 102.

= (3.99 - 0.00047) x 102

= 3.98953 x 102

Three hundred thousand = 300000

In 300000, there is no decimal point. So, assume there is a decimal point at the end.

300000.

Add the decimal point after the first nonzero digit.

3.00000

The decimal point is shifted five digits to the left. Take 5 as exponent for 10 and 105 can be used to write the given number in standard form.

300000 = 3.0 x 105

Five million = 5000000

In 5000000, there is no decimal point. So, assume there is a decimal point at the end.

5000000.

Add the decimal point after the first nonzero digit.

5.000000

The decimal point is shifted six digits to the left. Take 6 as exponent for 10 and 106 can be used to write the given number in standard form.

5000000 = 5.0 x 106

= 5000000 x 3000

= (5.0 x 106) x (3.0 x 103)

= (5.0 x 3.0) x (106 x 103)

= 15 x 106 + 3

= 15 x 109

= 1.5 x 10x 109

= 1.5 x 101 + 9

= 1.5 x 1010

= 2500 kilograms

= 2500 x 1000 grams

= 2500000 grams

= 2.5 x 106 grams

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